Assignment:
Consider harmonic oscillators with mass in, spring constant k, and damping coefficient b. For the values specified,
(a) Find the general solution of the second-order equation that models the motion of the oscillator;
(b) Find the particular solution for the given initial condition; and
(c) Using the equations for the solution of the initial-value problem, sketch the y(t)and v(t)-graphs. Compare these graphs to your sketches for the corresponding exercise.
- m = 1, k = 7, b = 8, with initial conditions y(O) = -1, v(0) = 5
- m = 1, k = 8, b = 6, with initial conditions y(O) = 1, v(0) = 0
- m = 1, k = 5, b = 4, with initial conditions y(O) = 1, v(0) = 0
- m = 1, k = 8, b = 0, with initial conditions y(0) = 1, v(0) = 4
Provide complete and step by step solution for the question and show calculations and use formulas.